论文标题
现实生活中金融市场复杂动态的2D征费飞行模型
A 2D Levy-flight model for the complex dynamics of real-life financial markets
论文作者
论文摘要
我们报告了S \＆P 500指数价格的每日关闭值及其建模的日常闭合值的时间演变中的出现。通过使用随机矩阵理论中的极值统计数据，我们提出的模型的功效得到了验证和验证。我们发现，在2D价格空间中，每对股票的随机演变是一种规模不变的复杂轨迹，其曲折度受$ 2/3 $几何定律的控制，旋转半径$ r_g（t）$与总长度$ \ ell（t）$ \ ell（t）$ r_g（t），I.e.我们构建了一个WishArt矩阵，该矩阵包含所有库存，直至特定的变量时期，并在30年内查看其光谱属性。与标准的随机矩阵理论相反，我们发现特征值的分布随着时间的推移而有一个幂律尾部，指数会减少，这是时间相关性的定量指标。我们发现，与原始索引$α= 3/2 $的2DLévy飞行距离的时间演变产生相同的经验光谱特性。该模型最大的特征值和观察结果的统计数据完全一致。
We report on the emergence of scaling laws in the temporal evolution of the daily closing values of the S\&P 500 index prices and its modeling based on the Lévy flights in two dimensions (2D). The efficacy of our proposed model is verified and validated by using the extreme value statistics in random matrix theory. We find that the random evolution of each pair of stocks in a 2D price space is a scale-invariant complex trajectory whose tortuosity is governed by a $2/3$ geometric law between the gyration radius $R_g(t)$ and the total length $\ell(t)$ of the path, i.e., $R_g(t)\sim\ell(t)^{2/3}$. We construct a Wishart matrix containing all stocks up to a specific variable period and look at its spectral properties over 30 years. In contrast to the standard random matrix theory, we find that the distribution of eigenvalues has a power-law tail with a decreasing exponent over time -- a quantitative indicator of the temporal correlations. We find that the time evolution of the distance of a 2D Lévy flights with index $α=3/2$ from origin generates the same empirical spectral properties. The statistics of the largest eigenvalues of the model and the observations are in perfect agreement.
